I've nothing against my past math teachers, but it's safe to say that for me, math was something created by dead mathematicians. I had to memorize their thoughts and apply them to page 134. I got A's in math, but that doesn't mean that I understood what I was doing. It doesn't mean that I was doing the practice of mathematics either.
I recently spent a day at a math workshop. One of the instructors talked briefly about the shift that is taking place or must take place in math instruction. She likened math to Language Arts. Language Arts is not punctuation, grammar, word choice, etc. Language Arts is putting those things into practice by putting pen to the paper and writing for real purposes. Math is not skills, facts, algorithms, and procedures. Math is putting those things into the practice of mathematics by problem solving, modeling, and communicating.
It's safe to say that for too long, math has been about skills, facts, algorithms, and procedures. We haven't shown our students that they're actually supposed to use those things as tools to mathematize their own world. They're supposed to practice mathematics, just like they would practice writing, to see that they're creating math and making sense of it, not leaving the job to some dead mathematicians from long ago. I haven't fully figured out how to make this happen yet. Quotes like this one leave me with all sorts of questions. I know I'm heading in the right direction though. I can identify bits and pieces of it in my room and say, "That's what they're talking about." I'm on a mission to discover how to make sure my mathematicians are always doing the practice of mathematics. Wish me luck!